surface example

3D Log Bowl Surface Graph

A bowl that rises slowly as it moves outward.

z = log(1 + x^2 + y^2)

Teacher prompt

Why does the bowl flatten far from the center?

The logarithm grows slowly, so added distance changes height less and less.

min z 0.00max z 0.0056 samples

What this graph represents

The logarithm compresses large distance values.

Where it appears in calculus

This makes growth-rate comparison visual.

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Related graphs

Open another surface page and compare shape, slices, and contour behavior.

Saddle Surface

z = x^2 - y^2

A saddle surface curves up in one direction and down in the perpendicular direction.

Gaussian Surface

z = exp(-(x^2 + y^2))

A smooth bell-shaped surface centered at the origin.

Elliptic Paraboloid

z = x^2 + y^2

A bowl-shaped surface that opens upward.

Inverted Paraboloid

z = 12 - x^2 - y^2

A dome-shaped surface with a highest point at the center.